Multiplying device



April 16, 1940. w -r LANG 2,196,996

MULTIPLYING DEVICE Filed Feb. 7. .1939

WuI LEJ" T Lung Patented 16, 1940 UNi'l'ED STATES PATENT. omcs SClaims.

(Granted underthe m of March 3, ms, as

mended April 8 The invention described herein may be manufactured and used by or for the Government for governmental purposes, without the payment to me of any royalty thereon.

' This invention relates to a multiplyin device of simple and emcient construction, adapted for use in any desired situation where it is required that one quantity be multiplied by another quantity to give a product mechanically.

It is an object of the invention to provide a multiplying device largely comprised of standard parts to facilitate construction and maintenance.

It is a further object of the invention to employ parts, which are not standard; that may be ll easily constructed.

It is a still further object of the invention to provide anorganization of elements, comprising the multiplier, in such fimctional relation relative to each other that they may be readily shiftgo ed relative to each other in a particular design of machine wherein the multiplier is to be employed.

The specific nature of the invention as well as other obiects and advantages thereof will clearly appear from a description of a preferred embodigg ment as shown in the accompanying drawing in which:

Fig. '1 is a diagrammatic plan view of the multip er:

Fig. 2 is a diagrammatic view in elevation on line 2-2 of Pig. 1. a

' Referring to the drawing, and more particularly to Fig. 1, it will be seen that three differentials generally indicated at I, I and 20 and two cams II and iii are used in the multiplier to perform the essential operations. v Diiferentials i and I may be of a well known bevel geartype.

The differential l includes the usual planet bevel gears i and 4 carried on a spider ii fixed to the shaft I ancl crown bevel gears 8 and I freely rotatably journaled on or relative to shaft 5' in meshing relation with planet gears I and 4.

The crown bevel gear or wheel l has integral therewith, or otherwise suitably attached thereto,

a a driving bevel or other gear I. Likewise crown bevel gear or wheel I has worm wheel or other gear a suitably secured thereon. The shaft I on which spider II is fixed extends away from crown wheel I any suitable distance and is secured to a so cam it which will hereinafter be referred to in more detail.

Differential I may be of the same type as differential i and identical in construction therewith; consequently, a detailed description of differential l' is not believed to be desirable. line for rotation and has bevel or other suitable gears i4 and II fixed thereon which cooperate with the bevel gears 8 and 8', respectively. The gears I4 and ii are of such size and so arranged on shaft I! in meshing relation with gears 8 and 8', respectively, as to impart equal and opposite angular displacements to the bevel gears 8, 8' and crown wheels of the differentials attached tothe latter upon rotation of shaft i2.

The shaft i3 is also mounted for rotation and has fixedly secured thereto worms or other suitable gearing i6, I! which cooperate, respectively, with-the worm wheels or gears 9 and 9' for rotating the same upon rotation of shaft [3. The ratios between both worms and worm wheels are the same so that rotation of shaft It will eil'ect equal angular displacement of crown wheels I and I and the pitch of the worm gearing is such that shaft It may be reversibly rotated and that rotation of both the worm wheels will be in the same direction as that of the shaft.

From the description thus far it will be apparent that shaft It may be rotated through an angle proportional to a given quantity which will in turn rotate the crown wheels I and I in the same direction through a corresponding angular value. Likewise, shaft I! may be rotated through an angle proportional to a given quantity but in this case due to the disposition of the gearing on shaft I! the crown wheels 6 and 8' will be rotated in opposed directions equal amounts corresponding to the quantity through which shaft i2 was rotated. The differentials will. therefore, "in

one case add the quantities transmitted to the transmitted thereto by means of its planet wheels 3, and 4 and spider H to shaft 5 which is ang'u larly displaced an amount equal to or proportional to this difference. It is obvious, however, that the function of the differentials may be interchanged to suit conditions by reversing the rotation of shaft l2 or |3 or reversing the relation of gears I4 and i5 or relatively reversing gears 1 and l with respect to each other.

Cams IO and I0, attached for rotation to the output shafts 5 and 5 of differentials i and I, respectively, are substantially identical in construction; accordingly, the description of cam Ill may be regarded as the description of cam III also. Cam I0 is a simple two-dimensional planar cam having a symmetrical peripheral cam surface so shaped that its lift or throw is proportional .to the square of the angle through which the cam is rotated when it is rotated about its axis in either one of opposite directions from a normal zero position. A cam of this type is well adapted to the use in hand as it is symmetrical and offers no obstacle to the employment of standard machine practice in fabrication.

Followers l8 and I8 are are suitably mounted for reciprocation on lines passing through the centers of 'rotation of cams l0 and I0, respectively, and engage or follow the surfaces of the cams. Each of the followers is provided with a rack, respectively, indicated at I9 and I9. As mentioned in the description prior hereto, cam ID will be rotated angularly by differential an amount proportional to the sum of the two quantities transmitted to the differential and that portion of cam surface beneath the follower i8 will lift the follower a distance proportional to the square of the sum of these quantities, for the surface of the cam is designed to have a lift proportional to the square of its angular displacement. Similarly, cam It! will lift follower IS a distance proportional to the square of the difference of the quantities as differential rotates the cam through an angle proportional to this difference.

An additional differential 20, which may be of the same type as differentialsl and I or a common spur gear type as shown, is interposed between the followers I8 and I8. This differential may comprise a casing 2|, shafts 22 and 23, and spur gears 24 and 25 within the casing fixed to the shafts 22 and 23, respectively. Extending from the side walls of the casing are .axles 26 and 21 which carry the pinions 28 and 29, respectively. Pinion 28 meshes with gear 25 and pinion 29 and pinion 29 also meshes with gear 24. Circumferentially disposed about casing 2| is a ring gear 30. Shaft 22 has a gear 3| engaging rack l9 and shaft 23 has gear 32 engaging rack IS. A gear 33 of proper ratio relative to ring gear 30 meshes with the latter.

Movement of the follower I8 and its rack I! will rotate gear 32 an angular distance proportional to the square of the sum of the two quantities through which shafts |2 and I3 have been rotated, and movement of rack I8 will cause gear 3| to subtract from' the angular movement of casing 2|, as effected by gear 32, an amount equal to the square of the difference of the two quantities through which shafts I2 and I3 have been rotated. As a result of the algebraic combination of the quantities by differential 20, the casing 2|, and ring gear 30 will be displaced angularly an amount proportional to the algebraic differenceof the squares of the sum of the quantities and the difference of the quantities which shafts I2 and I3 have been rotated, which angular displacement of ring gear 30 is directly proportional to the product of the quantities.

Gear 33 may be of such size and suitably connected to a shaft 34 for transmitting the product to any desired point for actuating other mechanism, or the shaft may be provided with an index or properly graduated scale to cooperate with a scale or index respectively, from which the product may be directly read or otherwise discerned.

The shafts l2 and I3 may, through proper connection, be made operable by any mechanism having movements that is desired to multiply. Alternatively, the shafts l2 and/or |3 may be manually rotated in accordance with two quantities to be multiplied, in which case suitable indices, and graduated scales will be used to guide and govern the operator in actuating the shafts.

The operation of the multiplier is believed to be apparent from the above detailed description; however, to follow the operation of the device in multiplying one quantity by another, let it be assumed that it is desired to multiply quantity a by quantity b. Shaft l2 will be rotated through an angle corresponding to quantity 1) and shaft I3 will be rotated through an angle corresponding to quantity a. Because of the relation of gears l4 and i5 to differentials and I respectively, the differential I will add quantity a to quantity b and differential I will subtract quantity b from quantity a. Shaft 5 will be angularly displaced (a+b) and shaft! will be angularly displaced (a-b) to angularly displace the cams connected therewith corresponding amounts. Since the cams are designed to lift the followers a distance proportional to the square of the angles through which the cams have been rotated, the cam ill will raise follower l8 a distance proportional to (a-i-b) or, in expanded form of the quantity, a distance equal to The cam l0 will raise follower l8 a distance proportional to (a-b)" or, in expanded form of the quantity, 9. distance equal to (a 2ab+b Differential algebraically combines the quantities (aH-Za-b-l-b) and (a 2a-b+b to angularly displace ring gear 30 an amount proportional to or equal to 4ab, or in direct proportion to the product a-b. Gear 33 may be of such ratio with respect to gear 30 as to transmit the product 11-?) directly to shaft 34.

It is to be noted that each of the factors may be either a positive or a negative number, the directions of rotations of shafts l2, l3 and 3| for negative numbers being opposite to that for positive numbers.

In accordance with the provisions of the patent statutes the principle of operation, together with apparatus now considered to represent a preferred embodiment of the invention has been disclosed, but it is to be understood that the apparatus shown is by way of illustration and not of limitation. Any suitable mechanism may be substituted for the differentials, that will comblue the quantities being multiplied in the desired manner, or the combinations may be effected manually.

What I claim as new and desire to secure by Letters Patent of the United States, is:

1, In a device for multiplying one factor by another, a pair of shafts displaceable in accordance with said factors respectively, means interconnected with said shafts for proportionally combining the sum and the difference of the displacements thereof and including output and additional output means foralgebraically combining the lifts of said cams.

2. In a device for multiplying one factor by another, a pair of shafts displaceabie in accordance with said factors respectively, means interconnected with said shafts for combining the sum and the difference of the displacements thereof and including output shafts displaceable in accordance with said sum and difference, a symmetrical cam secured to each of said output shafts for displacement therewith, said cams each being provided with a planar lifting surface disposed in its plane of displacement and having a lift proportional to the square of its displacement and output means for algebraically combining the lifts of said cams.

3. In a device for multiplying one factor by another, a pair of shafts displaceable in accordance with said factors respectively, means interconnected with said shafts for combining the sum and the difference 'of the displacements thereof and including output shafts rotatable in accordance with said sum and difference, a symmetrical cam secured to each of said output shafts for rotation therewith, said cams each being provided with a peripheral "planar lifting surface disposedin its plane of rotation and having a lift proportional to the square of its rotation, followers engaging said cam surfaces for movement thereby and means including an additional output shaft for algebraically combining the lifts of said followers and'driving said last named output shaft a fractional proportion thereof.

WALTER T. LANG. 

